Quantum geometry and gravitational entropy

Details Quantum geometry and gravitational entropy Quantum geometry and gravitational entropy

2007-05-30

arxiv.org/abs/0705.4431v2

JHEP 0712:067,2007

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 2 figures; references added

Scientific paper

10.1088/1126-6708/2007/12/067

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

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